MinT - Best Known (40, 40+65, s)-Nets in Base 16

Best Known (40, 40+65, s)-Nets in Base 16

(40, 40+65, 225)-Net over F₁₆ — Constructive and digital

Digital (40, 105, 225)-net over F₁₆, using

net from sequence [i] based on digital (40, 224)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
  - a function field by GarcÃa and Quoos [i]

(40, 40+65, 6967)-Net in Base 16 — Upper bound on s

There is no (40, 105, 6968)-net in base 16, because

1 times m-reduction [i] would yield (40, 104, 6968)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 169555 365890 013620 835972 024832 326827 902676 557149 952055 222354 190407 056683 399483 997228 546271 053404 058633 238045 796014 512989 816991 > 16¹⁰⁴ [i]